In this paper, we are mainly concerned with the cross-correlations between individual stocks in financial markets.
Previous researches have revealed that the cross-correlation between stocks
fluctuates over time [1]}, [2]}, [3]}.
In particular, it could be enhanced during the recession of business cycles.
Similarly, the international correlation
is stronger in a volatile period.
Based on the time-lag cross-correlations, one
obtains that changes in singular eigenvectors and eigenvalues
are the largest during a financial crisis [4]}.
Further, individual stocks may form communities due to the cross-correlations between stocks.
A community is also called a business sector, since its stocks usually share common economic properties.
For example, the business sectors have been investigated with the random matrix theory (RMT), in the mature markets such as the American stock market
and Korean stock market [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, and also in the
emerging markets such as the Chinese stock market and Indian stock market [11]}, [12]}, [13]}.
In the emerging stock markets, both standard and unusual business sectors are detected.
The RMT theory may identify the business sectors in a financial market,
but it could not draw the interactions between
the business sectors. Especially, the global price movement in a stock market is usually much stronger than the local one.
To uncover the local interactions between the business sectors, therefore, it is necessary to develop a proper method
to subtract the global price movement.
On the other hand, the structure of financial networks has been gaining
increasing interests [14]}, [15]}, [16]}. For example, the correlation structure of individual stocks
has been investigated with the minimal spanning tree (MST) and planar
maximally filtered graph (PMFG) [17]}, [18]}, [19]}, [20]}, [21]}, [22]}.
